What is C-rate?

The charge and discharge current of a battery is measured in C-rate. Most portable batteries are rated at 1C. This means that a 1000mAh battery would provide 1000mA for one hour if discharged at 1C rate. The same battery discharged at 0.5C would provide 500mA for two hours. At 2C, the 1000mAh battery would deliver 2000mA for 30 minutes. 1C is often referred to as a one-hour discharge; a 0.5C would be a two-hour, and a 0.1C a 10-hour discharge.
The capacity of a battery is commonly measured with a battery analyzer. If the analyzer's capacity readout is displayed in percentage of the nominal rating, 100% is shown if a 1000mAh battery can provide this current for one hour. If the battery only lasts for 30 minutes before cut-off, 50% is indicated. A new battery sometimes provides more than 100% capacity.

When discharging a battery with a battery analyzer that allows the setting of different discharge C-rates, a higher capacity reading is observed if the battery is discharged at a lower C-rate and vice versa. By discharging the 1000mAh battery at 2C, or 2000mA, the analyzer is scaled to derive the full capacity in 30 minutes. Theoretically, the capacity reading should be the same as with a slower discharge, since the identical amount of energy is dispensed, only over a shorter time. Due to internal energy losses and a voltage drop that causes the battery to reach the low-end voltage cut-off sooner, the capacity reading may be lowered to 95%. Discharging the same battery at 0.5C, or 500mA over two hours may increase the capacity reading to about 105%. The discrepancy in capacity readings with different C-rates is related to the internal resistance of the battery.

One battery that does not perform well at a 1C discharge rate is the portable sealed lead-acid. To obtain a reasonably good capacity reading, manufacturers commonly rate these batteries at 0.05C or 20 hour discharge. Even at this slow discharge rate, a 100% capacity is hard to attain. To compensate for different readings at various discharge currents, manufacturers offer a capacity offset. Applying the offset to correct the capacity readout does not improve battery performance; it merely adjusts the capacity calculation if discharged at a higher or lower C-rate than specified.

Lithium-ion/polymer batteries are electronically protected against high load currents. Depending on battery type, the discharge is limited to between 1C and 2C. This protection makes the lithium ion unsuitable for biomedical equipment and power tools demanding high inrush currents.

Depth of discharge

The typical end-of-discharge voltage for nickel-based batteries is 1V/cell. At that voltage level, roughly 99% of the energy is spent and the voltage starts to drop rapidly if the discharge continued. Discharging beyond the cut-off voltage must be avoided, especially under heavy load.

Since the cells in a battery pack cannot be perfectly matched, a negative voltage potential, also known as cell reversal, will occur across a weaker cell if the discharge is allowed to continue uncontrolled. The more cells that are connected in series, the greater the likelihood of cell reversal occurring.

Nickel-cadmium can tolerate some cell reversal, which is typically about 0.2V. During that time, the polarity of the positive electrode is reversed. Such a condition can only be sustained for a brief moment because hydrogen evolution on the positive electrode leads to pressure build-up and possible cell venting. If the cell is pushed further into voltage reversal, the polarity of both electrodes is being reversed and the cell produces an electrical short. Such a fault cannot be corrected.

Some battery analyzers apply a secondary discharge (recondition) that discharges the battery voltage to a very low voltage cut-off point. These instruments control the discharge current to assure that the maximum allowable current, while in sub-discharge range, does not exceed a safe limit. Should cell reversal develop, the current would be low enough not to cause damage. Cell breakdown through recondition is possible on a weak or aged pack.

If the battery is discharged at a rate higher than 1C, the end-of-discharge point of a nickel-based battery is typically lowered to 0.9V/cell. This compensates for the voltage drop induced by the internal resistance of the cells, wiring, protection devices and contacts. A lower cut-off point also produces better capacity readings when discharging a battery at cold temperatures.

Among battery chemistries, nickel-cadmium is least affected by repeated full discharge cycles. Several thousand charge/discharge cycles are possible. This is why nickel-cadmium performs well on power tools and two-way radios that are in constant use. nickel-metal-hydride is less durable in respect to repeated deep cycling.

Lithium-ion typically discharges to 3.0V/cell. The spinel and coke versions can be discharged to 2.5V/cell to gain a few extra percentage points. Since the equipment manufacturers do not specify the battery type, most equipment is designed for a 3-volt cut-off.

A discharge below 2.5V/cell may put the battery's protection circuit to sleep, preventing a recharge with a regular charger. These batteries can be restored with the Boost program available on the Cadex C7000 Series battery analyzers.

Some lithium-ion batteries feature an ultra-low voltage cut-off that permanently disconnects the pack if a cell dips below 1.5V. A very deep discharge may cause the formation of copper shunt, which can lead to a partial or total electrical short. The same occurs if the cell is driven into negative polarity and is kept in that state for a while.

Manufacturers rate the lithium-ion battery at an 80% depth of discharge. Repeated full (100%) discharges would lower the specified cycle count. It is therefore recommended to charge lithium-ion more often rather than letting it discharge down too low. Periodic full discharges are not needed because lithium-ion is not affected by memory.

The recommended end-of-discharge voltage for lead-acid is 1.75V/cell. The discharge does not follow the preferred flat curve of nickel and lithium-based chemistries. Instead, Lead-acid has a gradual voltage drop with a rapid drop towards the end of discharge.

The cycle life of sealed lead-acid is directly related to the depth of discharge. The typical number of discharge/charge cycles at 25°C (77°F) with respect to the depth of discharge is:

• 150 - 200 cycles with 100% depth of discharge (full discharge)
  
• 400 - 500 cycles with 50% depth of discharge (partial discharge)
  
• 1000 and more cycles with 30% depth of discharge (shallow discharge)

The lead-acid battery should not be discharged beyond 1.75V per cell, nor should it be stored in a discharged state. The cells of a discharged lead-acid sulfate, a condition that renders the battery useless if left in that state for a few days. Always keep the open terminal voltage at 2.10V and higher.

Discharge currents and load signatures

Rechargeable batteries are tolerant to wide range of load signatures. In terms of cycle life, a constant current discharge is better than a digital load. Figure 1 reveals the number of cycles a nickel-metal-hydride battery provides at different load conditions. As can be seen, the capacity loss is greatest on a digital load, such as a cell phone. Increased internal resistance is the principal cause of premature failure.

Figure 1: Cycle life of nickel-metal-hydride batteries under different operating conditions. (Zhang, 1998) NiMH performs best at DC and analog loads and has lower cycle life with digital a load.

Although rechargeable batteries provide good overall loading capabilities, the cycle count is higher if the discharge current is kept moderate. Figures 2 shows permanent capacity losses under a 1C, 1.3C and 2C discharge. The test was performed on a lithium-ion battery. Other chemistries show a similar wear-and-tear phenomenon at loads above 1C.

Figure 2: Cycle life of lithium-ion at varying discharge levels. (Choi et al., 2002) Like a mechanical device, the wear-and-tear of a battery increases with higher loads

What constitutes a discharge cycle?

There are no standard definitions that constitute a discharge cycle. Smart batteries that keep track of discharge cycles commonly use a depth-of-discharge of 70% to define a discharge cycle. Anything less than 70% does not count. The reason of the cycle count is to estimate the end-of-battery life.

A battery often receives many short discharges with subsequent recharges. With the smart battery, these cycles do not count because they stress the battery very little. On satellites, the depth-of-discharge is only about 10%. Such minute discharge cycles put the least amount of stress on the batteries in space. With shallow discharges, however, nickel-based batteries require a periodic deep discharge to eliminate memory.

Lithium and lead-based batteries do not require a periodic full discharge. In fact, it is better not to discharge them too deeply but charge them more often. Using a larger battery is one way to reduce the stress on a battery.

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© Copyright 2003 - 2005 Isidor Buchmann